47. The function f : [0, 3] [1, 29], defined by f(x) = 2x 3 15x 2 + 36x + 1, is
(A) one-one and onto (B) onto but not one-one
(C) one-one but not onto (D) neither one-one nor onto
the given function is
differentiating the function wrt x,
thus the function is increasing from 0<x<2,
and then decreasing from x=2 to x=3
it is not monotonically increasing or decreasing.
thus the function is not one-one.
now we will check the image of the function at critical points.
therefore the function is onto, but not one-one.